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Geometry: Seeing, Doing, Understanding
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ByMolly Crockeron April 14, 2004
I am teaching from this book this year, having taught from the second edition for the last several years. I wouldn't use any other geometry book besides Mr. Jacobs'. There are some typos in the 1st printing of the 3e, but nothing serious.
This book is more relaxed on proof-writing than the 2e, and so I have added some proofs from the 2e to supplement it. There are also a few exercises each lesson from the 2e that require more algebra, and so I use those, too. Another instructor could do as well if they added SAT problems from a SAT practice book.
The teacher guide is spectacular, providing a richness in both the history of geometry and its application. Did you know that the Greeks not only knew how far away the moon was, but also that its orbit is a bit elliptical? (Who needs technology to be smart?)
The publisher generated tests are not written by Mr. Jacobs, and are frankly for weenies. If the publisher doesn't remedy that situation I'll be writing my own for next year. When the tests are changed, the book will have my 5-star rating. If you're homeschooling, use the summary and review as the chapter tests.
This book is more relaxed on proof-writing than the 2e, and so I have added some proofs from the 2e to supplement it. There are also a few exercises each lesson from the 2e that require more algebra, and so I use those, too. Another instructor could do as well if they added SAT problems from a SAT practice book.
The teacher guide is spectacular, providing a richness in both the history of geometry and its application. Did you know that the Greeks not only knew how far away the moon was, but also that its orbit is a bit elliptical? (Who needs technology to be smart?)
The publisher generated tests are not written by Mr. Jacobs, and are frankly for weenies. If the publisher doesn't remedy that situation I'll be writing my own for next year. When the tests are changed, the book will have my 5-star rating. If you're homeschooling, use the summary and review as the chapter tests.
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ByDaniel S. Yateson October 10, 2003
"I have just spent a couple of hours browsing through Harold Jacob's GEOMETRY, and I think I've fallen in love again. This book is really lovely. What a treat. I didn't want to put it down. Harold has really done a masterful job of bringing in so much stuff -- culture, puzzles, challenges, current events, etc., and his use of cartoons and similar things that appeal to kids (like me!) is the best. This is a very rich and compelling guide through the central ideas of geometry. Harold has created a roadmap that will let learners experience the thrill and wonder and discovery of important geometrical truths. As a fellow author, I am inspired to work even harder to try to reach his standard of excellence. Congratulations to Harold and his editors on an OUTSTANDING contribution to mathematics learning." -
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ByPeter Renzon June 30, 2003
Amazon reviews let you know what teachers and students think about texts. Type in the following ISBNs to see the reviews of the second edition (ISBN 071671745X) of this text or of the author's Mathematics: A Human Endeavor (ISBN 071672426X). These comments on the third edition are based on close reading, not classroom experience. With an initial review up, I hope to see what others have to say.
I taught at Reed, Wellesley, and Bard Colleges and watched the reform mathematics program develop when I was associate director of the Mathematical Association of America, in Washington, DC. Geometry is my research area. I worked in publishing as an editor for more than 20 years. I have read every word of this book and worked all of the exercises because I was its freelance editor. I am a knowledgeable, interested party.
The third edition towers over the second edition, which is described by its most recent Amazon reviewer, Edward Lee, as "the best geometry text in existence, bar none" (January 25, 2003). Begin by noticing the use color throughout, then notice how color has been used to make key material in the text and diagrams stand out more clearly. Detailed comparisons will show you that every part of the book has been scrutinized and reworked, adding a host of new examples and exercises, fine-tuning the concepts and wording. Coordinates are used throughout, so that analytic methods are now another tool rather than the subject of a special chapter, late in the book.
Chapter 1, An Introduction to Geometry is completely new and shows the reader how geometry has been used from the dawn of history, in the East and the West, to design cities, measure the earth's circumference, design pyramids, and figure land taxes. This last brings us to the final lesson of this chapter, "We Can't Go on Like This." Here the student discovers that the Egyptian tax assessor's formula, though plausible, does not work. Something may look sensible and even be used, but we need to be careful and check things. Not everything that is plausible is true. And so we are off to Chapter 2 on deductive reasoning, and then on to all of geometry, including solid geometry (Chapter 15) and non-Euclidean geometry (Chapter 16) --- optional in most first courses.
Jacobs put all of his art into this revision. It is his best effort. Donald J. Albers begins his foreword "This is one of the great geometry books of all time. ... It is the finest example of instructional artistry I have ever encountered."
Geometry is a wild and beautiful subject. Think of it as a continent you might visit and explore. The lessons in this book are station stops on your tour. At each stop, Jacobs gives you a sense of what there is to see and explore. The exercise sequences are side trips for individuals or groups. It is these jaunts that give you a real feel for the place, they build the muscle you need for further exploration and show you small wonders or glimpses of distant peaks. Albers calls these exercises "the beating heart of the book."
Here is a side trip you can explore now: Take a lopsided quadrilateral and erect equilateral triangles on its sides so that their third vertices point alternatingly into and out of the quadrilateral. Connect these four new vertices in the order of the sides of the quadrilateral they are derived from. You will see that no matter what your original quadrilateral was, the new quadrilateral is of a very special sort. The exercise is straightforward, and the result is surprising. Some readers may want to understand the geometry that lies behind this observation. That goal is like the wish to scale a distant peak. Many may feel the call, but only some will set out and reach the summit. Geometric proofs, sometimes so mysterious, are our search for an answer to the question "Why?"
A Teacher's Guide with solutions to all the exercises, lesson plans, reduced size images of the transparency masters, and commentaries on the subject is available. There is also a separate Test Bank. The Transparency Masters, for teachers who use an overhead projector, are available on a CDROM.
In 10 years, I expect to see a crop of geometers who cut their teeth on this book. In the meantime, I expect to see many reviews from students and teachers on this site. Let this be the beginning.
I taught at Reed, Wellesley, and Bard Colleges and watched the reform mathematics program develop when I was associate director of the Mathematical Association of America, in Washington, DC. Geometry is my research area. I worked in publishing as an editor for more than 20 years. I have read every word of this book and worked all of the exercises because I was its freelance editor. I am a knowledgeable, interested party.
The third edition towers over the second edition, which is described by its most recent Amazon reviewer, Edward Lee, as "the best geometry text in existence, bar none" (January 25, 2003). Begin by noticing the use color throughout, then notice how color has been used to make key material in the text and diagrams stand out more clearly. Detailed comparisons will show you that every part of the book has been scrutinized and reworked, adding a host of new examples and exercises, fine-tuning the concepts and wording. Coordinates are used throughout, so that analytic methods are now another tool rather than the subject of a special chapter, late in the book.
Chapter 1, An Introduction to Geometry is completely new and shows the reader how geometry has been used from the dawn of history, in the East and the West, to design cities, measure the earth's circumference, design pyramids, and figure land taxes. This last brings us to the final lesson of this chapter, "We Can't Go on Like This." Here the student discovers that the Egyptian tax assessor's formula, though plausible, does not work. Something may look sensible and even be used, but we need to be careful and check things. Not everything that is plausible is true. And so we are off to Chapter 2 on deductive reasoning, and then on to all of geometry, including solid geometry (Chapter 15) and non-Euclidean geometry (Chapter 16) --- optional in most first courses.
Jacobs put all of his art into this revision. It is his best effort. Donald J. Albers begins his foreword "This is one of the great geometry books of all time. ... It is the finest example of instructional artistry I have ever encountered."
Geometry is a wild and beautiful subject. Think of it as a continent you might visit and explore. The lessons in this book are station stops on your tour. At each stop, Jacobs gives you a sense of what there is to see and explore. The exercise sequences are side trips for individuals or groups. It is these jaunts that give you a real feel for the place, they build the muscle you need for further exploration and show you small wonders or glimpses of distant peaks. Albers calls these exercises "the beating heart of the book."
Here is a side trip you can explore now: Take a lopsided quadrilateral and erect equilateral triangles on its sides so that their third vertices point alternatingly into and out of the quadrilateral. Connect these four new vertices in the order of the sides of the quadrilateral they are derived from. You will see that no matter what your original quadrilateral was, the new quadrilateral is of a very special sort. The exercise is straightforward, and the result is surprising. Some readers may want to understand the geometry that lies behind this observation. That goal is like the wish to scale a distant peak. Many may feel the call, but only some will set out and reach the summit. Geometric proofs, sometimes so mysterious, are our search for an answer to the question "Why?"
A Teacher's Guide with solutions to all the exercises, lesson plans, reduced size images of the transparency masters, and commentaries on the subject is available. There is also a separate Test Bank. The Transparency Masters, for teachers who use an overhead projector, are available on a CDROM.
In 10 years, I expect to see a crop of geometers who cut their teeth on this book. In the meantime, I expect to see many reviews from students and teachers on this site. Let this be the beginning.
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